What is a x-simple and y-simple region? [closed]

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In Vector Calculus by Marsden, Tromba, and Freedman, they define something called $x$- and $y$-simple regions in the chapter about Green's and Stoke's Theorem:

I have read the definition, but I do not quite understand what it means.

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1 Answer

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A region $D \subset \mathbb{R}^2$ is x-simple ($y$-simple) if every horizontal (vertical) line intersects $D$ in a line segment.

For example, the unit disk is $x$ and $y$-regular but an annulus is neither $x$ or $y$-regular as a line through the middle of the annulus intersects at two line segments, not a singular one.

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